How important is Trigonometry in High School?
You're in Class 11, just graduated from Class 10. All of a sudden, you realise topics are being taught in breakneck speed. You're trying your best to keep pace, but sometimes it can get overwhelming. And then, you're learning Trigonometry for the first time and you could probably do with some help.
I am Suman Mathews, online mathematics teacher and consultant. Having a double Master's in Mathematics and a teaching experience of three decades, teaching math to adolescents, I can help you with Trigonometry and Mathematics in general. You'll realise how easy Math is, after learning from me.
Trigonometry forms an integral part of Calculus. Trigonometric identities and concepts are used extensively in Differentiation and Integration. It's impossible to learn Calculus without first learning Trigonometry.
Measuring angles in Trigonometry
Until now, you've probably used degrees for measuring angles. The first concept in Trigonometry that you'll be introduced to is the concept of radian measure. Basically radian measure is how you measure angles.
You'll learn how to convert radians to degrees and vice versa. In this context, you'll also learn formulas on how to find the length of an arc of a circle and area of the sector of a circle. You need to note that these formulas use radian measure.
You have already learnt the basic trigonometric functions, namely, sine, cosine, tangent, cosecant, secant and cotangent. You learn the basic identities involving these. You also learn the basic graphs of the six trigonometric functions and their domain and range.
Sign of trigonometric functions
In Class 11, you'll learn the sign of the trigonometric functions in all the four quadrants. Remember
A S T C , in the first quadrant all trigonometric angles are positive, in the second quadrant, only sine is positive, in the third quadrant only tangent is positive and in the fourth quadrant only cosine is positive. "All Silver Tea Cups"(easy to remember)
Moving on, you'll proceed to learn about Trigonometric functions of Sum and Difference. In this context, you'll learn the formulas for sin(A+B), cos( A+B), tan (x+y), sin(x-y), cos(x-y) and tan(x-y). As a corollary to this, you will also learn about cot(x+y) and cot(x-y).
You'll also learn about negative angles, Note that sin(-x)=-sinx, cos(-x)=cosx, tan(-x)=-tanx. Also note that while measuring angles along the y axis, sin changes to cos, tan to cot and cosec to sec and vice versa. However, while measuring angles along the x axis, everything remains the same.
Converting Product into Sum/Difference and Vice Versa
You'll then proceed to learn the formulas of 2sinxcosy ,2cosxsiny, 2cosxcosy and 2sinxsiny. This is turn leads you to the formulas of sinx+siny, sinx-siny, cosx+cosy, Learn how to solve problems based on these.
Multiple and Sub Multiple Angles
This is an extremely important concept which is used extensively in Calculus. You learn about multiple and sub multiple angles here. An interesting point to note is that whatever works for 2x, will also work for x, only you need to divide the angle in the right hand side by 2.
Do you need extra help in Trigonometry?
Are you still a little shaky in Trigonometry? So, I offer online classes both one on one and group classes. You can choose to be helped in just one chapter of the entire curriculum.
I can help strengthen your concepts and problem solving abilities through multiple choice questions, case study based questions and more! You could team up with your friends and join me for group classes. That would be fun and interactive.
I hope this post helps you!